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Handbook of Differential Equations: Evolutionary Equations
 
 

Handbook of Differential Equations: Evolutionary Equations, 1st Edition

 
Handbook of Differential Equations: Evolutionary Equations, 1st Edition,C.M. Dafermos,Eduard Feireisl,ISBN9780444528483
 
 
 

Dafermos   &   Feireisl   

North Holland

9780444528483

9780080465654

652

240 X 165

Explore current theories of differential equations with a look to the future.

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Key Features

- Volume 1 focuses on the abstract theory of evolution
- Volume 2 considers more concrete probelms relating to specific applications
- Volume 3 reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear PDEs

Description

The material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear parabolic PDE's.
Articles will highlight the present as well as expected future directions of development of the field with particular emphasis on applications.
The article by Ambrosio and Savaré discusses
the most recent development in the theory of gradient flow of probability measures. After an introduction reviewing the properties of the Wasserstein space and corresponding subdifferential calculus, applications are given to evolutionary
partial differential equations. The contribution of Herrero provides a description of some mathematical approaches developed to account for quantitative as well as qualitative aspects of chemotaxis. Particular attention is paid to the limits of cell's
capability to measure external cues on the one hand, and to provide an overall description of aggregation models for the slim mold Dictyostelium discoideum on the other.
The chapter written by Masmoudi deals with a rather different topic - examples of singular limits in hydrodynamics. This is nowadays a well-studied issue given the amount of new results based on the development of the existence theory for rather general systems of equations in hydrodynamics. The paper by DeLellis addreses the most recent results for the transport equations with regard to possible applications in the theory of hyperbolic systems of conservation laws. Emphasis is put on the development of the theory in the case when the governing field is only a BV function.
The chapter by Rein represents a comprehensive survey of results on the Poisson-Vlasov system in astrophysics. The question of global stability of steady states is addressed in detail. The contribution of Soner is devoted to different representations of non-linear parabolic equations in terms of Markov processes. After a brief introduction on the linear theory, a class of
non-linear equations is investigated, with applications to stochastic control and differential games.
The chapter written by Zuazua presents some of the recent progresses done on the problem of controllabilty of partial differential equations. The applications include the linear wave and heat equations,parabolic equations with coefficients of low regularity, and some fluid-structure interaction models.

Readership

University libraries and Research mathematicians

C.M. Dafermos

Affiliations and Expertise

Brown University, Providence, RI, USA

View additional works by C.M. Dafermos

Eduard Feireisl

Affiliations and Expertise

Mathematical Institute AS CR, Prague, Czech Republic.

View additional works by Eduard Feireisl

Handbook of Differential Equations: Evolutionary Equations, 1st Edition

Preface

Contributors

1.L. Ambriosio, G. Savaré: Gradient flows of probability measures

2.M.A. Herrero: The mathematics of chemotaxis

3.N. Masmoudi: Examples of singular limits in hydrodynamics

4. C. DeLellis: Notes on hyperbolic systems of conservation laws and transport equations

5. G. Rein: Collisionless kinetic equations from astrophysics - the Vlasov-Poisson system

6. H.M. Stochastic representations for non-linear parabolic PDE's

7. E. Zuazua Controllability and observability of partial differential equations: Some results and open problems

Index

 
 
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